Pebbles

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

Great Squares

Investigate how this pattern of squares continues. You could measure lengths, areas and angles.

Square Areas

Can you work out the area of the inner square and give an explanation of how you did it?

Inscribed in a Circle

Stage: 3 Challenge Level:

The area of a square inscribed in a circle with a unit radius is, satisfyingly, $2$.

What is the area of a regular hexagon inscribed in a circle with a unit radius?

What is the area of an equilateral triangle inscribed in a circle with a unit radius?